Following to article of "Can We Solve a Nonlinear Equation with Many Variables?" posted on below link:
Let me start second example for an equation with four variables
as follows:
Example (2): Solving of Sphere
Equation
As you know, the sphere equation has
many applications in all fields of engineering and physics. When we talk about
a sphere equation, our discussion can be expanded not only macroscopic systems but also
microscopic particles such as the
quantum model of the Hydrogen atom. Therefore, let me start
by solving of a sphere equation for a limited domain and range as follows:
Consider the sphere equation with
below domain:
If
x^2 + y^2 + z^2 = r^2 x, y,z ϵ N, x, y,z ≤
100
Then the range for the radius of
sphere will be: r ϵ N, r ≤ 173
Now, I apply previous method and get
all results of "x, y, z" for "r" in given range. The number
of
results related to "r" has been presented on below graph:
In this case, total sum of possible
answers is only and only equal to 4935.
Above graph shows us that there is a
maximum number of answers equal to 165 for r = 99. For instance, I have brought
some results on below figure:
As we can see, for r =
15 and r = 150, the number of results are the same equal to 15 while for r = 31, we have 24
answers
We can apply this domain and range
as a template for all macroscopic and microscopic numbers.
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